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                  {\sanhao{\textbf{基于优化的传输线法的双稳态接触器的并行有限元分析}}}\\
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                  \textbf{杨文英$^1$, 彭飞$^1$, 刘洋$^1$}\\[2pt]
                  \small{(1电气学院，哈尔滨工业大学，黑龙江哈尔滨 150001；)}\\[2pt]
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                {\small{\textbf{摘~要：}如今，在工程当中，结构、力、热、电磁等物理场的分析过程中，有限元方法还是最主要的计算方法。对于需要进行大规模计算的研究者来说，如何提高有限元的计算效率始终是他们所关心的问题。在这篇文章当中，我们研究了一种优化的传输线方法，它使用了一种新的等效电路模型和松弛方法，并将它应用到了含永磁的轴对称接触器的有限元计算当中。为了加速每一迭代步的计算速度，我们使用了一种牛顿预处理器、并行的传输线反射过程和基于级别调度法的并行三角求解器来在CPU上实现加速过程。和传统的牛顿迭代法相比，所提出的的优化的传输线法将计算效率提升了十倍以上。另外，在所研究的接触器的模型当中，我们还计算了电磁吸力，通过和试验数据进行对比，验证了本文所提出的的方法的正确性。
                \\

                \textbf{关键字：}接触器；有限元分析；并行算法；永磁；静磁场\\
                \textbf{文献标志码：}A \hspace{4cm} \textbf{中国分类号：}TP18
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                  {\sanhao{\textbf{An Optimised Parallel Transmission Line Iteration for Finite Element Analysis of a Bistable Axisymmetrical Actuator}}}\\
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                  \textbf{Yang Wenying$^1$, Peng Fei$^1$, Liu Yang$^1$;}\\[2pt]
                  \small{(1 School of Electrical Engineering, Harbin Institute of Technology, Harbin 150001, Heilongjiang;)}\\[2pt]
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                {\small{\textbf{Abstract:}\quad Nowadays, finite element method (FEM) is still the mainstream tool in the analysis of structure, heat, fluid and electromagnetic processes. The improvement of computational efficiency in FEM is always an interest for researchers who need large-scale computation. In this paper, we investigate an optimised transmission line method (TLM) using an equivalent circuit model and relaxation method to calculate the nonlinear magnetostatic field in an axisymmetrical actuator with permanent magnet. A Newton-Raphson (N-R) preconditioner, parallel reflection phase in TLM and a CPU-based parallel triangular solver using level scheduler are exploited to accelerate the computation in each nonlinear iteration step. Compared with conventional N-R iteration, the optimised TLM algorithm greatly reduces the computation time more than 10 times. In addition, the magnetic field distribution and the electromagnetic force of the studied actuator are calculated by the proposed method in this paper, and the simulation results are validated through experiments.
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                \textbf{Keywords}\quad Actuators； Finite element analysis； Parallel algorithms；
Permanent magnets； Magnetostatics
}}
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           % \noindent{\footnote{\noindent {\textbf{收稿日期}：2017-05-30；\textbf{修回日期}
%          ：}
%          2017-07-16\\
%          \textbf{基金项目}：国家自然科学基金资助（610****3，8*****69），江西省
%          科技计划项目(No. 2011*******87)\\ \textbf{作者简介
%          }：
%        张三（1992-），男，硕士研究生，主研：智能信息处理、大数据应用；李四，
%      男，硕士，高级工程师，主研：气象通讯技术，计算机应用技术；}.
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